CaltechAUTHORS
  A Caltech Library Service

A Hausdorff-Young theorem for rearrangement-invariant spaces

Bennett, Colin (1973) A Hausdorff-Young theorem for rearrangement-invariant spaces. Pacific Journal of Mathematics, 47 (2). pp. 311-328. ISSN 0030-8730. http://resolver.caltech.edu/CaltechAUTHORS:BENpjm73

[img]
Preview
PDF
See Usage Policy.

1512Kb

Use this Persistent URL to link to this item: http://resolver.caltech.edu/CaltechAUTHORS:BENpjm73

Abstract

The classical Hausdorff-Young theorem is extended to the setting of rearrangement-invariant spaces. More precisely, if 1 <_ p <_ 2, p[-1] + q[-1] = 1, and if X is a rearrangement-invariant space on the circle T with indices equal to p[-1], it is shown that there is a rearrangement-invariant space X on the integers Z with indices equal to q[-1] such that the Fourier transform is a bounded linear operator from X into X. Conversely, for any rearrangement-invariant space Y on Z with indices equal to q[-1], 2 < q <__ oo, there is a rearrangement-invariant space Y on T with indices equal to p[-1] such that J is bounded from Y into Y. Analogous results for other groups are indicated and examples are discussed when X is L[p] or a Lorentz space L[pr].


Item Type:Article
Record Number:CaltechAUTHORS:BENpjm73
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:BENpjm73
Alternative URL:http://projecteuclid.org/Dienst/UI/1.0/Summarize/euclid.pjm/1102945868
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:554
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:18 Aug 2005
Last Modified:26 Dec 2012 08:40

Repository Staff Only: item control page